Numerical modeling of waves for a tsunami early warning system

Abstract
A numerical model based on the mild slope equation is applied to reproduce
the propagation of small amplitude transient waves over mildly sloped sea
bed. The model makes use of the Fourier transform to convert the time
dependent hyperbolic equation into a set of elliptic equations in the frequency
domain. Therefore the reproduction of the full frequency dispersion of waves
is achieved, since each frequency component is solved using a dedicated
elliptic equation.
The model results suitable to reproduce the tsunami far field propagation.
Tsunamis are traditionally considered extremely long, single waves able of
devastating the coast; however it has become well accepted that these kind of
waves is a wave packet, that in most cases may exhibit a frequency dispersive
behavior.
The results of available experimental studies on tsunami generated by
landslides are used to validate the model. In the present work the waves
generation is analyzed trough a wave-maker boundary condition, which
works as a wave paddle in the physical models, otherwise it is included in
the field equation. The mild slope equation is derived again taking into
account the movement of the sea bottom, thus in the equation appears
a forcing term which represents the effects of a tsunamogenic source.
Validation and discussion about the effects of the source term, for different
bottom movements, are presented. The comparison with other laboratory
experiments were used to gain insigth on tsunami generation and propagation
phenomena, and to test the model application in a tsunami early warning.
An important feature of the model, that in our opinion makes it suitable
to be used in early warning, is that can be applied in two stages: one is
extremely expensive from the computational point of view, the other is very
fast and can be applied in real-time. Therefore the idea, when setting up
an early warning system, is to define the scenarios and to perform the a
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